Self Number or Devlali Number or Colombian Number

The concept of Self number or Devlali number or Colombian number was introduced by D. R. Kaprekar (Dattatreya Ramchandra Kaprekar).

Self number or Devlali number or Colombian number is an integer that cannot be expressed as the sum of any other integer and its individual digits.

In other words, if any integer y cannot be expressed as the sum of any other integer n and its individual digits, then it is referred to as Self number or Devlali number or Colombian number.

Important Points

Point 1: All integer n less than 15 give the result less than 20.

Point 2: All integer n greater than or equal to 15 give the result greater than 20.

The Procedure

Step 1: Consider an integer y.

Step 2: Take any other integer n.

Step 3: Add integer n with its individual digits.

Step 4: If the sum is not equal to the original integer y taken in Step 1, then integer y is Self number or Devlali number or Colombian number, else not.

For Example

Integer y: 20

Take any other integer: 14.

Add integer 14 with its individual digits: 14 + 1 + 4 => 19.

Here the sum is not equal to the original integer 20, which means that integer 20 cannot be expressed as the sum of any other integer and its individual digits. Hence, integer 20 is Self number or Devlali number or Colombian number.

Integer y: 21

Take any other integer: 15.

Add integer 15 with its individual digits: 15 + 1 + 5 => 21.

Here the sum is equal to the original integer 21, which means that integer 21 can be expressed as the sum of any other integer and its individual digits. Hence, integer 21 is not considered as Self number or Devlali number or Colombian number.

Hope you have understood this amazing concept of Self number or Devlali number or Colombian number. In case of any issue, provide your valuable comments.